Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import bisect
l=[0]*50001
for i in range(50001):
    if i==0 or i==1:
        l[i]=i
    else:
        l[i]=l[i-1]+i
n=int(input())
i=bisect.bisect_left(l,n)
j=1
f=0
while i>=j:
    if l[i]+l[j]==n:
        f=1
        break
    elif l[i]+l[j]>n:
        i=i-1
    elif l[i]+l[j]<n:
        j=j+1
if f==1 or n==2:
    print('YES')
else:
    print('NO')